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21 st Century Lessons Evaluating Expression Primary Lesson Designers: Kristie Conners Sean Moran 1

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2 This project is funded by the American Federation of Teachers.

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3 *1 st Time Users of 21 st Century Lesson: Click HERE for a detailed description of our project.HERE 21 st Century Lessons – Teacher Preparation Spend AT LEAST 30 minutes studying the Lesson Overview, Teacher Notes on each slide, and accompanying worksheets. Set up your projector and test this PowerPoint file to make sure all animations, media, etc. work properly. Please do the following as you prepare to deliver this lesson: Feel free to customize this file to match the language and routines in your classroom.

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4 Lesson ObjectiveContent Objective: Students will be able to evaluate algebraic expressions. Language Objective: Students will be able to describe the steps to evaluating expressions. Lesson DescriptionThis lesson is designed to be implemented following the previous lessons in this unit. This lesson demonstrates how to evaluate algebraic expressions. The focus shows a process of substituting in numbers into any algebraic expressions and using the order of operations to evaluate the expressions; strategies which were highlighted in the previous lessons and used in this lesson. Lesson Overview (1 of 3)

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5 Lesson Vocabulary Substitution: Replace a variable with number. Evaluate: To calculate the value of a numerical or algebraic expression.. Materials Pencil, notebook, copies of the class work assignment, homework and exit slip. Index cards*, number cubes of different colors*. (Alternate suggestions given if do not have these supplies) Scaffolding This lesson models and scaffolds evaluating expressions. There is time in the lesson for students to copy the process into their notebook. Throughout the lesson, substitution is demonstrated with colors for visual learners. Also, the video links below is a great tool to use for your students, especially ELL students. Enrichment There are several opportunities for enrichment. During the activity, Can’t Wait To Evaluate, the teacher can create their own spinner. This will allow your students to use integers and rational numbers to make the activity more challenging. If your students are proficient with rational numbers, a second Can’t Wait To Evaluate activity is provided for additional challenge. Online Resources for Absent Students Practice http://www.ixl.com/math/grade-6/evaluate-variable-expressions-with-whole-numbers http://www.ixl.com/math/grade-6/evaluate-variable-expressions-involving-decimals- fractions-and-mixed-numbers http://www.ixl.com/math/grade-6/evaluate-multi-variable-expressions http://www.ixl.com/math/grade-6/evaluate-expressions-involving-integershttp://www.ixl.com/math/grade-6/evaluate-expressions-involving-integers (enrichment) Videos http://learnzillion.com/lessons/468-evaluate-onestep-algebraic-expressions-by-substitution http://learnzillion.com/lessons/468-evaluate-onestep-algebraic-expressions-by-substitution (one step) http://learnzillion.com/lessons/469-evaluate-multiple-step-algebraic-expressions-by- substitutionhttp://learnzillion.com/lessons/469-evaluate-multiple-step-algebraic-expressions-by- substitution (multi-step) Lesson Overview (2 of 3)

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6 Lesson Overview (3 of 3) Common Core State Standard 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. 6.EE.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s 3 and A = 6s 2 to find the volume and surface area of a cube with sides of length s = ½. Before and AfterThis lesson is the fifth lesson in the unit. This lesson should be presented following the previous lessons. This lesson will continue to build off of the lessons in this unit and understand the process in evaluating algebraic expressions by substitution. Topic BackgroundThe link below gives a small background on the history of Algebra. This is also a great opportunity to connect topics covered in social studies with mathematics. http://www.ehow.com/video_4977241_who-invented- algebra.html

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Warm Up Agenda 7 OBJECTIVE: SWBAT evaluate algebraic expressions. Language Objective: SWBAT describe the steps to evaluating expressions. A magic store is selling exploding pens for $3 each plus $1 for tax. Do you agree or disagree? Explain. Kyle thinks you can figure out the cost of 10 pens with the below. Click to reveal next part

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Agenda: OBJECTIVE: SWBAT evaluate algebraic expressions. Language Objective: SWBAT describe the steps to evaluating expressions. 1) Warm Up 2) Launch 3) Explore- 1 4) Explore- 2 5) Practice 6) Assessment 8 Individual Shopping with Marvin- Whole Class/Pairs Class work: Can’t Wait to Evaluate – Groups Exit Slip- Individual Evaluating with Marvin- Whole Class Practice with Formulas- Whole Class

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Launch- Shopping with Marvin Agenda 9 Marvin the Math Magician has a problem for you. How much will Marvin have to pay for 12 wands and 7 hats? He wants to buy some magic wands and some magician hats. The wands cost $8 each and $5 for each hat.

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Agenda 10 How much will Marvin have to pay for 12 wands and 7 hats? The wands cost $8 each and $5 for each hat. How did you get your answer? How can we write a to show our answer of 131? Click to reveal next part Launch- Shopping with Marvin

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Explore 1- Evaluating with Marvin Agenda 11 How much will Marvin have to pay for 6 wands and 3 hats? Remember: the wands cost $8 each and $5 for each hat. Click to reveal next part Write an numerical expression to find the answer.

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Agenda 12 What changed in the two examples? Sometimes it helps to represent a problem as an The wands cost $8 each and $5 for each hat. w= # of wands h= # of hats Click to reveal next part 12 wands 7 hats 6 wands 3 hats 12 7 6 3 7 6 3 Explore 1- Evaluating with Marvin

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Agenda 13 10 2 w h This is called substitution!! Click to reveal next part We just evaluated the expression. evaluate w = 10h = 2 How much will Marvin have to pay for 10 wands and 2 hats? Explore 1- Evaluating with Marvin

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Agenda 14 w = 10h = 2 How much will Marvin have to pay for 10 wands and 2 hats? 10 2 This is called substitution!! Click to reveal next part We just evaluated the expression. evaluate Explore 1- Evaluating with Marvin

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Agenda 15 w= h= 9 7 w h Find the cost of buying 9 wands and 7 hats. Steps: 1. Copy the expression. 2. Substitute the value in for the variable. 3. Evaluate using the order of operations. Click to reveal next part 9 7 Explore 1- Evaluating with Marvin

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Explore 2- Formulas Agenda 16 Flashback… Click to reveal next part Objective: evaluate algebraic expressions. For example: engineers, architects and builders use geometric formulas every day. Circumference Volume Rectangular Prism Surface Area Cylinder We can use the process of evaluating to solve problems in the real world.

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Explore 2- Formulas Agenda 17 Volume is the amount of space a shape takes up. The expression for calculating the volume of the rectangular prism is below. Find the volume 9 ft 4 ft 5 ft Click to reveal next part Steps: 1. Copy the expression. 2. Substitute the value in for the variable. 3. Evaluate using the order of operations. or

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9 ft 4 ft 5 ft Agenda 18 Surface Area is the total of the area of all sides. The expression for calculating the surface area of a rectangular prism is below. Find the volume. Click to reveal next part Steps: 1. Copy the expression. 2. Substitute the value in for the variable. 3. Evaluate using the order of operations. Explore 2- Formulas

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Practice- Class work Agenda 19 Can’t Wait To Evaluate! Directions: Each group receives a set of Evaluation Cards along with two different colored number cubes. Before starting, the team decides which color cube stands for which variable. (Example: the red cube replaces a, the green cube replaces b.) One person in the group rolls the number cubes. Students use the numbers to evaluate the expression. a=____b=____

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Summary Agenda 20 a=____b=____ Click each problem for demonstration Can’t Wait To Evaluate!

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Exit Slip Agenda 32 Kiara was asked to evaluate the expression. Her answer was 14. Did she substitute 11, 13, or 15? How do you know? Answer : 13 27 – 13 14

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Back to Lesson 33 1 st Time Users of 21 st Century Lessons Welcome to 21 st Century Lessons! We are a non-profit organization that is funded through an AFT (American Federation of Teachers) Innovation Grant. Our mission is to increase student achievement by providing teachers with free world-class lessons that can be taught via an LCD projector and a computer. 21 st Century Lessons are extremely comprehensive; we include everything from warm–ups and assessments, to scaffolding for English language learners and special education students. The lessons are designed into coherent units that are completely aligned with the Common Core State Standards, and utilize research-based best practices to help you improve your students’ math abilities. Additionally, all of our lessons are completely modifiable so you can adapt them if you like. Description of 21 st Century Lessons: Next Slide

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34 1 st Time Users of 21 st Century Lessons The lesson that you are currently looking at is part of a unit that teaches the following Common Core Standards: Standards for This Unit Next SlideBack to Lesson Expressions and Equations 6.EE Apply and extend previous understandings of arithmetic to algebraic expressions. 1. Write and evaluate numerical expressions involving whole-number exponents. 2. Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = ½. 3. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. 4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are

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35 1 st Time Users of 21 st Century Lessons In order to properly use 21 st Century Lessons you will need to possess or arrange the following things: Required: PowerPoint for P.C. (any version should work) Note: Certain capabilities in the PowerPoint Lessons are not compatible with PowerPoint for Mac, leading to some loss of functionality for Mac PowerPoint users. An LCD projector Pre-arranged student groups of 2 – (Many lessons utilize student pairings. Pairs should be seated close by and be ready to work together at a moment’s notice. Scissors – at least 1 for every pair Requirements to teach 21 st Century Lessons: Next SlideBack to Lesson

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36 1 st Time Users of 21 st Century Lessons Computer speakers that can amplify sound throughout the entire class “Calling Sticks” – a class set of popsicle sticks with a student’s name on each one A remote control or wireless presenter tool– to be able to advance the PowerPoint slides from anywhere in your classroom Personalize PowerPoints by substituting any names and pictures of children we included in the PowerPoint with names and pictures of your own students. Since many lessons utilize short, partner-processing activities, you will want a pre- established technique for efficiently getting your students’ attention. (“hands- up”, Count from “5” to “0” etc.) Project onto a whiteboard so you or your students can solve problems by hand. (Lessons often have a digital option for showing how to solve a problem, but you may feel it is more effective to show the work by hand on a whiteboard.) Internet connectivity – without the internet you may not have full functionality for some lessons. Strongly Suggested to teach 21 st Century Lessons: Next SlideBack to Lesson

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37 1 st Time Users of 21 st Century Lessons We suggest spending 30-45 minutes reviewing a lesson before teaching it. In order to review the lesson run the PowerPoint in “Slideshow “- Presenters View and advance to the “Lesson Overview” slide. By clicking on the various tabs this slide will provide you with a lot of valuable information. It is not necessary to read through each tab in order to teach the lesson, but we encourage you to figure out which tabs are most useful for you. Note: All of our lessons are designed to be taught during a 45-55 minute class. If your class is shorter than this you will have to decide which sections to condense/remove. If your class is longer we suggest incorporating some of the “challenge” questions if available. Lesson Preparation (Slide 1 of 2) Next Slide Back to Lesson

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38 1 st Time Users of 21 st Century Lessons After reviewing the overview slide, click your way through the PowerPoint. As you go, make sure to read the presenter note section beneath each slide. The note section is divided into two sections: “In-Class Notes” and “Preparation Notes.” The In-Class Notes are designed to be concise, bulleted information that you can use “on the fly” as you teach the lesson. Included in In-Class Notes are: a) a suggested time frame for the lesson, so you can determine whether you want to speed up, slow down, or skip an activity, b) key questions and points that you may want to bring up with your students to get at the heart of the content, and c) answers to any questions being presented on the slide. The Preparation Notes use a narrative form to explain how we envision the activity shown on the slide to be delivered as well as the rationale for the activity and any insight that we may have. Lesson Preparation (Slide 2 of 2) Next SlideBack to Lesson

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39 1 st Time Users of 21 st Century Lessons There are several features which have been incorporated into our PowerPoint lessons to help make lessons run more smoothly as well as to give you access to additional resources during the lesson should you want them. These features include: Agenda Shortcuts – On the agenda slide, click on any section title and you will advance to that section. Click the agenda button on any slide to return to the agenda. Action Buttons – On certain slides words will appear on the chalk or erasers at the bottom of the chalkboard. These action buttons give you access to optional resources while you teach. The most common action buttons are: Scaffolding – gives on-screen hints or help for that slide Answers – reveals answers to questions on that slide Challenge – brings up a challenge questions for students Agenda – will return you to the agenda at the beginning of the lesson Features built into each PowerPoint lesson Back to Lesson

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The goal of 21 st Century Lessons is simple: We want to assist teachers, particularly in urban and turnaround schools, by bringing together teams of exemplary educators to develop units of high-quality, model lessons. These lessons are intended to: Support an increase in student achievement; Engage teachers and students; Align to the National Common Core Standards and the Massachusetts curriculum frameworks; Embed best teaching practices, such as differentiated instruction; Incorporate high-quality multi-media and design (e.g., PowerPoint); Be delivered by exemplary teachers for videotaping to be used for professional development and other teacher training activities; Be available, along with videos and supporting materials, to teachers free of charge via the Internet. Serve as the basis of high-quality, teacher-led professional development, including mentoring between experienced and novice teachers. 21 st Century Lessons The goal… 40

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Directors: Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues Committee Ted Chambers - Co-director of 21st Century Lessons Tracy Young - Staffing Director of 21st Century Lessons Leslie Ryan Miller - Director of the Boston Public Schools Office of Teacher Development and Advancement Emily Berman- Curriculum Director (Social Studies) of 21st Century Lessons Carla Zils – Curriculum Director (Math) of 21 st Century Lessons Brian Connor – Technology Coordinator 21 st Century Lessons The people… 41

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